Book description
Fourier analysis is one of the most useful and widely employed sets of tools for the engineer, the scientist, and the applied mathematician. As such, students and practitioners in these disciplines need a practical and mathematically solid introduction to its principles. They need straightforward verifications of its results and formulas, and they need clear indications of the limitations of those results and formulas.Principles of Fourier Analysis furnishes all this and more. It provides a comprehensive overview of the mathematical theory of Fourier analysis, including the development of Fourier series, "classical" Fourier transforms, generalized Fourier transforms and analysis, and the discrete theory. Much of the author's development is strikingly different from typical presentations. His approach to defining the classical Fourier transform results in a much cleaner, more coherent theory that leads naturally to a starting point for the generalized theory. He also introduces a new generalized theory based on the use of Gaussian test functions that yields an even more general yet simpler theory than usually presented.
Principles of Fourier Analysis stimulates the appreciation and understanding of the fundamental concepts and serves both beginning students who have seen little or no Fourier analysis as well as the more advanced students who need a deeper understanding. Insightful, nonrigorous derivations motivate much of the material, and thoughtprovoking examples illustrate what can go wrong when formulas are misused. With clear, engaging exposition, readers develop the ability to intelligently handle the more sophisticated mathematics that Fourier analysis ultimately requires.
Table of contents
 Cover
 Half Title
 Title Page
 Copyright Page
 Table of Contents
 Preface
 Sample Courses
 I Preliminaries

II Fourier Series
 8 Heuristic Derivation of the Fourier Series Formulas
 9 The Trigonometric Fourier Series
 10 Fourier Series over Finite Intervals (Sine and Cosine Series)
 11 Inner Products, Norms and Orthogonality
 12 The Complex Exponential Fourier Series
 13 Convergence and Fourier’s Conjecture
 14 Convergence and Fourier’s Conjecture: The Proofs
 15 Derivatives and Integrals of Fourier Series
 16 Applications

III Classical Fourier Transforms
 17 Heuristic Derivation of the Classical Fourier Transform
 18 Integrals on Infinite Intervals
 19 The Fourier Integral Transforms
 20 Classical Fourier Transforms and Classically Transformable Functions
 21 Some Elementary Identities: Translation, Scaling and Conjugation
 22 Differentiation and Fourier Transforms
 23 Gaussians and GaussianLike Functions
 24 Convolution and Transforms of Products
 25 Correlation, SquareIntegrable Functions and the Fundamental Identity
 26 Generalizing the Classical Theory: A Naive Approach
 27 Fourier Analysis in the Analysis of Systems
 28 MultiDimensional Fourier Transforms
 29 Identity Sequences
 30 Gaussians as Test Functions and Proofs of Important Theorems

IV Generalized Functions and Fourier Transforms
 31 A Starting Point for the Generalized Theory
 32 Gaussian Test Functions
 33 Generalized Functions
 34 Sequences and Series of Generalized Functions
 35 Basic Transforms of Generalized Fourier Analysis
 36 Generalized Products, Convolutions and Definite Integrals
 37 Periodic Functions and Regular Arrays
 38 Pole Functions and General Solutions to Simple Equations
 V The Discrete Theory
 Tables, References and Answers
 Index
Product information
 Title: Principles of Fourier Analysis, 2nd Edition
 Author(s):
 Release date: December 2016
 Publisher(s): CRC Press
 ISBN: 9781498734134
You might also like
book
Fourier Transforms
Fourier Transforms: Principles and Applications explains transform methods and their applications to electrical systems from circuits, …
book
Introduction to Probability
Developed from celebrated Harvard statistics lectures, Introduction to Probability provides essential language and tools for understanding …
book
Understanding Digital Signal Processing
Amazon.com’s TopSelling DSP Book for Seven Straight Years—Now Fully Updated! is quite simply the best resource …
book
Python OneLiners
Python OneLiners will teach you how to read and write “oneliners”: concise statements of useful functionality …